An almost linear Robinson unification algorithm

Abstract

Further asymptotical improvement of original Robinson's unification idea is presented. By postponing the so-called occur-check in Corbin and Bidoit's quadratic rehabilitation of the Robinson algorithm at the end of unification an almost linear unification algorithm is obtained. In the worst case, the resulting algorithm has the time complexity O(p · A(p)), where p is the size of input terms and A is the inverse to the Ackermann function. Moreover, the practical experiments are summarized comparing Corbin and Bidoit's quadratic algorithm with the resulting almost linear unification algorithm based on Robinson's principle.